MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

18.9.5 Skeletonlike OCTAHEDRON

Folding angle of profile 3 is 109,47123º, twice as much as angle α in Point

18.2.2.2.

18.10 Perforated PENTAGONAL-DODECAHEDRON

C = 12 ; V = 20 ; A = 30

To optimise paper use, start with an argentic rectangle close in size to an A4, and follow

up this process:

1- To divide both sides of that argentic rectangle in 10 equal parts to get 100 small

argentic rectangles like the one outlined in Fig. 1.

2- Zigzag draw the diagonals of those 100 rectangles and then clear out their small

sides. (Recall Point 10.1.3).

The bases of those pyramids are

shown in Fig. 2 (Figs. 1 and 2 are not to

the same scale); in it we can see 4 cuts in-

dicated by dotted lines. Finally place one

base against the other, turn around and

interlock both domes (Fig. 3).

C

O

E F A

2

B

h h

3

O

B

Fig. 1 is the finished octahedron (inter-

nal folds of corners are not shown for the sake

of simplicity). It has a structure similar to that

of the tetrahedron in Fig. 7, Point 18.7: to con-

struct this octahedron we require 6 paper cor-

ners for the vertices (Fig. 2), and 12 cardboard

profiles for the sides (Fig. 3).

Vertices should be glued for fixing in

areas such as OAF and also where Figs. 2 and

3 meet. The crease of Fig. 3 will lie under OC

in the assembly.

Profiles to Fig. 3 may have any length

(as long as all of them are equal) but they

should keep the right proportion with the cor-

ners.